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Comparison study of methods on modeling covariance matrix in longitudinal data
Journal of the Korean Data & Information Science Society 2023;34:255-77
Published online March 31, 2023;
© 2023 Korean Data and Information Science Society.

Ha Gyeong Gong1 · Keunbaik Lee2

12Department of Statistics, Sungkyunkwan University
Correspondence to: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2022R1A2C1002752). This paper was prepared by extracting part of Ha Gyeong Gong’s thesis.
1 Graduate student, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea.
2 Professor, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea. E-mail:
Received December 26, 2022; Revised January 19, 2023; Accepted January 20, 2023.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In contrast to cross-sectional data analysis, longitudinal data analysis can explain the association between repeated outcomes when determining the influence of covariates on responses. To demonstrate this, a high-dimensional covariance matrix is used and it should be positive definite. However, estimating the covariance matrix is challenging. To overcome the restrictions, we assume the covariance matrix with a relatively simple structure. This assumption is too strong, though, and using a wrong covariance matrix can make the estimation of covariate effects biased. Recently three decomposition methods of the covariance matrix have been proposed. In this paper, we present the methods and compare the performance of the methods.
Keywords : High-dimensional, longitudinal data, positive definite, repeated outcomes.